EP 0 829 015 B1 discloses recording dangerous changes in the dielectric strength of insulation. In this case, only the partial voltage of a capacitive divider present between the measuring tap and ground potential is recorded as the electrical measured quantity and monitored for a change in the partial voltage. Obviously, a number of measured values, for example the amplitude of the partial voltage respectively at successive points in time, are recorded and stored. The temporal interval between two successive detected changes in the partial voltage is ascertained and the frequency of the changes occurring per unit of time is used as a basis for concluding the insulating state of the capacitor bushing. The point in time of a change must be recorded as accurately as possible. This requires great measurement effort, since the measured values must be ascertained at temporally very short intervals. Additionally, the deviation of the operating voltage from a nominal value has an effect on the accuracy of the evaluation, since a deviation of the operating voltage from its nominal value also has the consequence of a deviation of the corresponding partial voltage. This is disadvantageous in particular during a sustained change in the operating voltage.